Depth sensing indentation and methodology for mechanical property measurements

ABSTRACT

An indentation measurement apparatus is retrofittable onto any of a variety of load-applying frames and includes a mount for mounting an indenter of any geometry (for example blunt or sharp). The arrangement is very stiff and mechanical values including Young&#39;s modulus, strain hardening exponent, yield strength, and hardness can be obtained from a single load/unload versus displacement test. A wide variety of materials can be tested using the apparatus. An optical probe can measure displacement of the indenter head relative to a sample. A new method of calculating strain hardening directly from load/displacement measurement is presented as is a new method of calculating strain hardening exponent.

FIELD OF THE INVENTION

The present invention relates generally to measuring mechanicalproperties of materials, and more particularly to indentation testingwith the purpose of measuring such properties as hardness, yieldstrength, strain hardening exponent, and Young's modulus.

BACKGROUND OF THE INVENTION

The testing of mechanical properties of materials is a well-studied art.Standard tests exist for measuring mechanical properties such as Young'smodulus, strain hardening exponent, yield strength, hardness, and thelike, and many materials have been carefully characterized in terms ofmechanical properties. One set of techniques for determining mechanicalproperties in materials involve tests in the macro regime in which, forexample, a sample of material is stretched and its overall mechanicalresponse inferred in terms of stress and deformation. These and othertechniques have served, and continue to serve, an important role indetermining critical mechanical properties so that careful processingand selection of materials for use in a variety of industrial settingscan be made.

The above-described techniques, however, typically require large samplesof material and generally are destructive of those samples. There is anincreasing need in the field of materials science for analysis ofsmall-scale samples in a manner that can be essentially non-destructive.The increasing rate of miniaturization in the semiconductor field,increasing interest in thin coatings for optical, electronic, magnetic,and mechanical devices, and increasing use of functionally-gradedmaterials have led to a need for in situ testing of mechanicalproperties in small-scale structures. Additionally, there is interest inprobing properties of individual phases, grain boundaries, andinterfaces between phases and properties of novel materials such asnanocrystalline materials, or laminated or fibrous composites.

Indentation testing has developed as a viable technique for determiningcertain properties in a variety of materials at a very small scale,essentially non-destructively. Indentation testing typically involvesplacing a sample to be tested on a stage and applying a load to asurface of the sample via an indenter so as to slightly deform orpenetrate the surface, followed by removal of the load. Severaltechniques can be employed to derive certain properties of the materialfrom characteristics of the interaction of the indenter with thematerial. One set of techniques involves measuring an area ofindentation during or after indentation, for example, optically,refractively, via surface profilometry, etc. U.S. Pat. Nos. 4,627,096(Grattoni, et al.), 4,945,490 (Biddle, Jr. et al.), 5,284,049(Fukumoto), 5,355,721 (Las Navas Garcia), 5,483,621 (Mazzoleni),5,486,924 (Lacey), 4,852,397 (Haggag), 5,490,416 (Adler), 3,822,946(Rynkowski), and others follow this procedure. For example, the measuredarea of indentation can be used to determine a simple "flow" or hardnessvalue for the material, which is defined as the load applied divided bythe projected area of the indentation. Or, the dimension of any cracksformed in the sample surface can be measured to determine the toughnessof the material. Alternatively, the depth of penetration of the indenteras a function of applied load can be measured, and calculationsperformed to estimate roughly some mechanical properties. As discussedbelow, these techniques, in the prior art, have disadvantages.

Various shapes of indenters, for example spherical, cone-shaped, andpyramidal geometries can be used in indentation testing. Sharp indenters(e.g., cone-shaped and pyramidal) can be used in conventional tests toapply a load to a sample surface to form an imprint, or until thesurface cracks, followed by measurement of the area of imprint ordetermination of the crack length to measure hardness or toughness,respectively. One piece of indentation testing equipment utilizing asharp indenter at ultra low loads is sold by Nano Instruments, Inc. asthe Nanoindenter™ indentation tester. The Nanoindenter™ is a relativelycomplex, self-contained unit including an indenter system, a sharpindenter, a light optical microscope, a moveable x-y table, and acomputer. Analysis of load/depth curves with loads of less than oneNewton and displacement of less than one μm using a three-sidedpyramidal indenter is most typically carried out.

Blunt indenters, for example those having a surface contacting thesample surface that is spherical, are advantageous for use inindentation testing under certain circumstances for several reasons.First, less sample-destructive analyses often can be carried out.However, with blunt (spherical) indenters, sensitivity problems aremaximized since displacement of the sensor into the sample surface, at aparticular applied load, is less than displacement with a sharpindenter. This is especially problematic in measuring very softmaterials. Spherical indenters have, therefore, found most use intechniques in which load is applied to a sample surface and the diameterof the indentation formed thereby is measured using, for example,optical means.

U.S. Pat. No. 4,820,051 (Yanagisawa, et al.) discloses self-containedapparatus for measurement of the hardness of materials. A load isapplied to a sample via a sharp indenter (having a tip with a radius ofcurvature between 0.01 and 0.1 μm), and the displacement of the indenterrelative to the sample is determined. An optical sensing mechanismdetermines the penetration depth of the indenter. Yanagisawa, et al.measure load/displacement values only during application of the load,with a self-contained unit, and measure only hardness of the material.Yanagisawa, et al. measure penetration and, with knowledge of theindenter geometry and assuming that no pile-up or sinking-in of thematerial at the contact perimeter occurs (which is known to be a factorthat must be taken into account for accurate measurement), appear tocalculate what the area of the indentation would be without sinking-inor pile-up, to measure hardness. Measurements are made in a load rangeof less than one Newton.

Gattoni, et al. (U.S. Pat. No. 4,627,096) recognize that sinking-induring indentation testing should be taken into account when measuringhardness of a sample (see, e.g., FIGS. 1 and 4). Therefore, Gattoni, etal. illuminate the sample carrying the impression and optical processingequipment is used to determine the contact area between the indenter andthe sample.

U.S. Pat. No. 4,699,000 (Lashmore, et al. describes self-containedapparatus and methods for determining hardness. Displacement of theindenter into the sample as a function of time, using sharp indentergeometries, is made and a load versus displacement curve is therebyderived. Lashmore, et al., measure penetration and, with knowledge ofthe indenter geometry and assuming no pile-up or sinking-in, calculatethe area of the indentation (column 5, lines 5-43) to measure hardnessusing a self-contained unit. The displacement sensor of Lashmore, et al.is quite removed spatially from the indenter (FIGS. 2, 3). Lashmore, etal. state that modulus, yield strength, impact, hardness, creep andfatigue also can be determined. No indication, however, is given as tohow to go about determining these properties or whether, using thedescribed techniques, accurate determination of these properties can bemade.

U.S. Pat. No. 5,133,210 (Lesko, et al.) exploits thermal expansion inapplying a load to a sample surface via a spherical indenter. Variousmeasurements of load versus penetration (displacement) are made andtheories are presented as to how various mechanical properties can bederived. However, Lesko, et al. do not take into account sinking-in orpile-up of material at the contact perimeter. Additionally, it appearsfrom FIG. 5 of Lesko and theoretical analysis (Col. 5, lines 35-39 andCol. 4, lines 50-53) of Lesko, et al., that the assumption is made thatthe plastic regime of the load/displacement curve is linear. Thisassumption ignores the known non-linearity of the strain hardeningexponent. Lesko, et al. do not show experimental data supporting theevaluation of Young's modulus from a load/displacement curve. Moreover,the displacement sensor is quite removed spatially from the indenter(FIG. 3 of Lesko). Only ball indenters, and self-contained units, aredescribed. Measurements are made in the 1000 Newton range. It is unclearhow the methodology of Lesko, et al. would be applied to measurement atlow loads.

U.S. Pat. No. 5,490,416 (Adler) describes indentation of surfaces ofmaterials using a spherical indenter to determine hardness. Load isapplied to a sample via the indenter, but no load/depth relationship isexperimentally obtained. In an effort to accurately take into accountsinking-in and pile-up of material at the contact perimeter, arelatively time-consuming and labor-intensive process is carried outinvolving multiple indentation tests where the profile of theindentation is traced after each test with a surface analyzer todetermine the depth and diameter of the indentation. Adler mentions thatother devices may be used to measure the depth while load is beingapplied. However, no specific experimental arrangements are described indetail. No indication is given that any mechanical properties aremeasured directly from any portion of a load/displacement curve.Additionally, the theoretical framework relied upon assumes only plasticmaterial properties.

U.S. Pat. No. 4,852,397 (Haggag) describes a self-contained fieldindentation microprobe that measures load and penetration depth dataduring both loading and unloading cycles to determine flow propertiesand fracture toughness of a structure. The described apparatus isspecifically designed for use in the field to determine mechanicalcharacteristics of large samples, for example, a damaged pressure vesselor tank car. Haggag uses ultrasonic analyzers to measure thickness,internal presence of cracks, and pile-up around indentation aftertesting, and uses a video camera to measure an indentation formed fromload applied with a spherical indenter. Haggag states that the slope ofthe unloading portion of a load/displacement curve can be used as ameasure of elastic properties, but nowhere does Haggag describederivatization of area of indentation from a load/displacementmeasurement. Measurement in the kiloNewton range and above is made.

Accurate determination of the area of an indentation formed duringindentation testing, especially during loading, can be critical toaccurate determination of several mechanical properties of a sample. Onedrawback of prior art indentation testing techniques is thatdetermination of the area of the indentation formed while load isapplied either is not made precisely, or requires relatively complicatedapparatus. Prior indentation testing typically involves either formingan indentation, removing the indenter, and observing the size of theimprint with, for example, an optical microscope, profilometer, or thelike (which adds a step to analysis and cannot account for elasticrebound of the material after unloading, which typically issignificant), or indentation depth is measured and the area ofindentation calculated with mere knowledge of the geometry of theindenter (which is an approximation that fails to take into accountmaterial pile-up or sinking-in, which is almost always relevant andaffects the evaluation of mechanical properties), or involvescomplicated optical apparatus (such as that used by Grattoni, et al.,U.S. Pat. No. 4,627,096).

Additionally, most known techniques cannot accurately determineproperties of a sample in the elastic and plastic regimes within asingle test. Moreover, most prior art techniques involveload/displacement analysis either at very low loads (in the nanoregime), or at very high loads (tens or hundreds of kilograms), but donot provide the capability of sampling load/displacement characteristicsof a variety of materials over a very wide range of loads to determinelocal as well as bulk properties.

Therefore, it is an object of the invention to provide apparatus andmethods for indentation testing that allows for simple, relativelyuncomplicated and inexpensive, and accurate measurement of a variety ofmechanical properties. It is another object of the invention to provideindentation testing apparatus that can determine several mechanicalproperties in a single test or series of tests accurately, andreproducibly. It is another object of the invention to provideindentation testing apparatus that can sample materials accurately atvery low loads, but is also capable of operating over a wide range ofloads so that mechanical characterization of a material in the bulk aswell as local regime can be carried out. It is another object of theinvention to provide such apparatus in which indenters of a variety ofshapes and sizes can be used. It is another object of the invention toprovide a methodology and corresponding theoretical framework directlycoupled to in situ load/displacement measurement using a variety ofindenter shapes and sizes to derive mechanical properties.

SUMMARY OF THE INVENTION

The present invention provides apparatus and methodology for measuringmechanical properties of materials via indentation testing. According toone aspect, the invention involves deriving an accurate area of contactbetween an indenter and a sample during indentation testing, from theload/depth relationship resulting from the test. The load/depthrelationship is included in data provided from an indentation test inwhich load is applied to a surface of a sample of material with anindenter to cause the indenter to penetrate the surface to a depth. Theload/depth relationship is defined by depth of penetration of theindenter into the sample as a function of load applied to the sample viathe indenter. The area of contact is derived from the load/depthrelationship directly, that is, without observing the area of contactbetween the indenter and the sample during or after penetration. Thearea derived thereby includes area of contact due to pile-up of samplematerial around the indenter, or takes into account sinking-in of thematerial. The providing step can involve providing earlier-recorded datathat has been stored electronically, for example in a computer or on acomputer recording medium such as a disk, can involve providing datafrom a remote testing site electronically, can involve analyzing aplotted load/depth relationship, or the like. Additionally, theproviding step can involve measuring the data locally (i.e. at the samelocation at which the area of contact is derived, and using apparatus inelectronic communication with the deriving apparatus) by applying to thesample a load via an indenter and measuring penetration of the indenterinto the sample as a function of applied load. The apparatus can includea stage for mounting a sample, an indenter, a load cell, and a sensorconstructed and arranged to determine displacement of the indenterrelative to a sample on the stage.

According to another embodiment, the invention involves usingindentation testing apparatus to probe a sample of material having anelastic strain limit σ_(y) /E of less than about 0.05 with a bluntindenter, and deriving Young's modulus of the material from the initialloading portion of the load/depth relationship obtained during probing.The load/depth relationship is established by measuring penetration ofthe indenter into the sample as a function of applied load. According toone embodiment, the radius of curvature of the blunt indenter is lessthan about 6 mm. The method can involve also deriving yield strengthand/or strain hardening exponent from the load/depth relationship.Young's modulus also can be derived from the initial unloading portionof the load/depth relationship.

According to another embodiment, the invention involves probing a sampleof material that has a stress-strain curve with a non-linear slope withan indenter, measuring penetration as a function of applied load, andderiving strain hardening exponent from the loading portion of theload/depth relationship.

According to another embodiment, the invention involves probing a sampleof material with a blunt indenter to obtain a load/depth relationship,and deriving strain hardening exponent of the material from theload/depth relationship.

The invention also provides a method that involves deriving one of yieldstrength or strain hardening exponent of a sample of material from aload/depth relationship obtained via an indentation test using a sharpindenter.

According to another embodiment of the invention, Young's modulus aridat least one of yield strength, strain hardening exponent, and hardnessof material is derived from a single load/depth relationship in anindentation test.

One aspect of the invention involves deriving the area of contactbetween the indenter and sample from the load/depth relationship of anyor all of the above-described methods, and using the area of contact soderived to derive Young's modulus, yield strength, tensile strength,strain hardening exponent, and/or hardness. The area of contact includesthe area due to pile-up of sample material at the periphery of contactbetween the indenter and the material, or takes into account sinking-inof the material due to indentation.

Any of the above-described methods can involve immobilizing a sample ofmaterial on a stage prior to or during an indentation testing. Accordingto one embodiment, the invention provides a method of indentationtesting involving immobilizing a sample on a stage, applying a load ofgreater than at least about one Newton via an indenter, and determininga load/depth relationship of the material. One way of immobilizing thesample can involve securing the sample to the stage by a clamp orbracket or other device that applies a force to the material having acomponent in the direction of the stage. The sample can be secured tothe stage after load is applied to the sample via the indenter. This caninvolve applying load via an indenter and, at any degree of appliedload, securing the sample by, for example, tightening a clamp thatclamps the sample to the stage. One embodiment involves securing thesample to the stage by, for example, tightening a clamp holding thesample on the stage, at maximum load. This can be particularlybeneficial in measuring properties during unloading.

According to another aspect, the invention provides indentation testingapparatus that is easily retrofittable into a separate load-applyingframe, that is, a load-applying frame that is not necessarily builtspecifically for indentation testing. According to one embodiment, theapparatus includes a stage for mounting a sample, an indenter mount, aload cell, and a displacement sensor constructed and arranged todetermine displacement of the indenter mount relative to the sample. Theapparatus is readily mountable in and removable from a load-applyingframe using common fasteners. According to one embodiment, thedisplacement sensor is positioned within about 5 cm of a point at whichan indenter carried by the indenter mount contacts a surface of a samplecarried by the stage. The indenter mount can be one constructed andarranged to mount a spherical indenter and, according to one embodiment,the displacement sensor is positioned within a distance of about 20times the diameter of the indenter from the point at which a sphericalindenter carried by the indenter mount contacts a surface of a samplemounted on the stage. When a spherical or other blunt indenter isemployed, an indenter mount of the invention can be used that has asurface that contacts the blunt indenter mounted therein that is harderand stiffer than steel. According to one embodiment, that surface is atleast twice as hard and stiff as the sample tested.

Another embodiment of the invention involves particularly accurateretrofittable indentation testing apparatus. According to thisembodiment, apparatus is provided including a stage, and indenter mount,a load cell, a displacement sensor, and is readily mountable in andremovable from a load-applying frame using common fasteners. Theapparatus is capable of determining a physical characteristic, from aload/depth relationship obtained by applying load to a sample on thestage via an indenter carried by the indenter mount and measuringpenetration of the indenter into the sample. The physical characteristiccan be one of Young's modulus, yield strength, tensile strength, strainhardening exponent, and hardness, and is determined with less than about20% error.

Other advantages, novel features, and objects of the invention willbecome apparent from the following detailed description of the inventionwhen considered in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of a typical uniaxial true stress-strain curverepresentative of knowledge in the art;

FIG. 2 illustrates schematically indentation testing apparatus of theinvention;

FIG. 3 illustrates schematically a mount for a spherical indenter;

FIG. 4 illustrates schematically apparatus for securing a sample to astage;

FIG. 5 is illustrative of a typical load/depth curve of a pyramidalindentation test;

FIG. 6 is illustrative of a typical load/depth curve of a sphericalindentation test;

FIG. 7 illustrates schematically indentation measuring apparatus of theinvention mounted in a load-applying frame and connected to automatedmeasurement and data collection and analysis equipment;

FIG. 8 is a block diagram of an example computer system which may beused to automate the practice of the present invention;

FIG. 9 is a block diagram of a memory system shown in FIG. 8;

FIG. 10 is a data flow diagram representative of methodology fordesigning and conducting and analyzing results in accordance with theinvention;

FIG. 11 is a flow chart describing how control data for conducting atest is determined from parameters of the test and equipment;

FIG. 12 is a flow chart describing how additional control data isdetermined and how a test is conducted for a sharp indenter;

FIG. 13 is a flow chart describing how additional control data isdetermined and a test is conducted for spherical indenters;

FIG. 14 is a flow chart describing how a load/displacement data isanalyzed to obtain a mechanical property information for a sharpindenter;

FIG. 15 is a flow chart describing how a load/displacement data isanalyzed to obtain a mechanical property information for a sphericalindenter;

FIG. 16 illustrates experimentally-measured load/displacement dataduring loading and unloading for a polycrystalline ceramic materialusing a Vickers pyramidal indenter;

FIG. 17 is a logarithmic plot of experimentally-measuredload/displacement of nickel using a spherical indenter; and

FIG. 18 illustrates experimentally-measured load/displacement data forloading of nickel using a Vickers pyramidal indenter, and comparisonwith a curve derived theoretically in accordance with the invention.

NOMENCLATURE

a_(max) : maximum contact radius of a spherical indenter at load

A_(max) : contact area of an indenter at maximum load

c: parameter that accounts for sinking-in or pile-up at the contactperimeter of a spherical indenter

C: elasto-plastic stiffness of pyramidal indenters

C*: coefficient to account for the shape of pyramidal indenters

O: diameter of a spherical indenter

D_(p) : minimum diameter of a spherical indenter to avoid plasticdeformation of a sample under load less than the resolution of thesystem

D_(c) : maximum diameter of a spherical indenter to avoid radialcracking of a sample under maximum indentation load

D_(c) ': minimum diameter of a spherical indenter to avoid ring crackingof a sample under maximum indentation load

E: Young's modulus of sample

E': Young's modulus of a spherical indenter

E*: combined effective Young's modulus (indenter and sample)

h: measured depth of an indenter relative to the surface of a sample(penetration; displacement)

h_(max) : measured maximum indentation depth (penetration; displacement)

h_(min) : depth resolution of the system

h_(min) ': elastic depth corresponding to the load resolution of thesystem

h_(m) : recommended maximum indentation depth for characterization of alayer or a grain of the sample

h_(r) : residual indentation depth after complete unloading

h_(s) : total size of a diamond pyramid indenter

h_(y) : maximum elastic depth of a spherical indenter

H: secant elasto-plastic modulus at 30% plastic strain

K: characteristic stress for the power law elasto-plastic behavior

K_(c) : critical stress intensity factor of a sample

n: uniaxial compression strain hardening exponent of sample

P_(av) : Mayer's hardness or average contact pressure at maximum load

P: load applied to sample via an indenter

P_(m) : maximum load of a sharp indenter to avoid radial cracking at thecorners of a pyramid indentation

P_(max) : maximum load applied to sample via an indenter

P_(min) : load resolution of the system

P_(y) : maximum elastic force of a spherical indenter ##EQU1## initialslope, at maximum load, of the load/depth unloading curve X: distancebetween the displacement sensor and the axis of an indenter

G: 22° for Vickers and 24.7° for Berkovich pyramid indenters

ε: true strain in uniaxial compression

ε_(max) : maximum characteristic plastic strain for a spherical indenter

ν: Poisson ratio of sample

ν': Poisson ratio of a spherical indenter

σ: true stress in uniaxial compression

σ_(u) : uniaxial, compressive, true stress at 30% plastic strain

σ_(y) : yield strength in uniaxial compression of sample

σ_(y) ': yield or failure strength of the spherical indenter

Φ: angle of deviation of normality of an indenter to sample surface

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides indentation testing methods and apparatusfor deriving information on mechanical properties of a sample ofmaterial without the requirement of observation of the imprint formed.The information is derived from data provided from an indentation test,which data can be obtained by probing a sample of material and derivingthe information, probing a sample of material, storing the dataelectronically, and providing the data at a later time and/or differentlocation and then deriving the information. The area of the imprint isobtained directly from load/displacement measurement, and accuratelytakes into account pile-up and sinking-in of material duringindentation. The apparatus is constructed to accurately measuredisplacement of an indenter during both loading and unloading of theindenter, even at relatively low loads, and can probe a sample usingvirtually any indenter geometry. Several mechanical properties can bedetermined in a single load/unload cycle and accuracy of determinationof several properties can be assessed by comparison between analysesusing different indenter geometries.

As mentioned, observation of an imprint formed during indentation is notrequired. This means that observing the imprint formed duringindentation, for example via optical apparatus arranged to provide avisual signal of the imprint through the indenter, or apparatus designedto determine an electromagnetic radiation signal reflected or refractedfrom the imprint, and the like is not required. Additionally, removal ofthe indenter and observation of the resulting imprint optically, viaprofiletry, and the like is not required. The invention providesmethodology for derivation of mechanical properties directly from thedisplacement of an indenter relative to a sample as a function ofapplied load. Obviating the need for observation of the imprint duringor after penetration is a significant improvement.

Indentation depth/load relations are measured in situ with the apparatusof the invention by monitoring the penetration of an indenter into apolished specimen over a range of applied loads. The determination ofthese relations using blunt (spherical or rounded tip) and sharpindenters (such as those having cone or pyramidal geometries, commonlyreferred to as Rockwell, Vickers or Berkovich indenters) enables thedetermination of fundamental mechanical properties such as Young'smodulus (E), strain hardening exponent (n), yield strength (σ_(y)), andmicrohardness (P_(av)). As is well known in the art, these propertiescan be obtained from certain data revealed by a stress-strain curve of asample, which can be obtained using standard macro scale tests. Atypical stress-strain curve is illustrated in FIG. 1. One major purposeof the present invention is to improve techniques for obtaining suchproperties using indentation testing.

A wide variety of samples such as metals, oxides, carbides, ceramics,glasses, polymers, composites, layered solids such as surface coatings,and similar materials can be measured. The methodology and apparatus ofthe invention focuses on isotropic, homogeneous, elastic andelasto-plastic materials at room temperature. According to one feature,isotropic strain hardening can be determined in elasto-plasticmaterials.

In addition to many research-type applications, the present apparatusand methodology can be used in routine industrial practice in inspectionof materials, potentially non-destructively, such as metallurgicaloperation on alloys (e.g., quenching, tempering, nitriding,case-hardening, and annealing) as well as to study variation of chemicalcomposition (e.g., through diffusion). Such examinations on smallcomponents make the inventive process quantitative.

The invention involves, according to preferred embodiments,determination of Young's modulus (E) from the unloading portion of aload/displacement curve where a sharp indenter is used and/or from theinitial portion of the load/depth measurement as well as from unloadingusing a spherical indenter; strain hardening exponent (n) from theloading portion of the load/displacement curve in a load range where thematerial behavior is non-linear using a spherical or sharp indenter; andyield strength σ_(y) from load/depth data as measured with a sphericalindenter. Yield strength data so obtained can be checked by the loadingportion of a sharp indentation test. The invention also involvescombination, or comparison, of any of these processes with knownmeasurement techniques.

Referring to FIG. 2, indentation testing apparatus 10 of the inventionis schematically illustrated as mounted in an existing laboratoryload-applying frame 12. According to a preferred embodiment, apparatus10 is axisymmetric, that is, symmetric about the axis of loading.Apparatus 10 includes an upper, indenter-carrying portion and a lower,sample-carrying portion. The upper portion includes an indenter assembly14 mounted securely on an indenter mount 16 which is fastened to a loadcell 18, which is in turn fastened to an upper mount 20 including anupper flange 22 adapted to be secured to the load-applying frame. Thelower, sample-carrying portion includes a fixture 24, a top, or stagesurface 26 of which defines a stage upon which a sample 28 is positionedfor testing, and against which the sample can be securely held with oneor more clamps, or brackets 30. The apparatus is arranged such that theindenter is positioned above a top surface 32 of sample 28. Top surface32 is desirably polished prior to analysis.

Fixture 24 is secured to a base support 34 by, for example, a threadedadjusting mount 36 that threads into fixture 24 and/or base support 34.Adjusting mount 36 is preferred, but not necessary. Fixture 24 can besecured directly to (or be integral with) base support 34. Asillustrated, a rotation grip 38 allows rotation of threaded adjustingmount 36, a lock nut 40 threaded on mount 36 can secure threadedadjusting mount 36 via frictional engagement with base support 34, and alock nut 42 threaded on mount 36 can secure threaded adjusting mount 36via frictional engagement with fixture 24. This arrangement allows forrotation of threaded adjusting mount 36 about a vertical axis to adjustthe distance between indenter assembly 14 and sample surface 32, andindependent adjustment of the rotational orientation of stage surface 26and sample 28 so that sensor 46 and mirror 48 (discussed below) can bealigned. As discussed below, a displacement sensor can also be adjustedindependently. Base support 34 includes a lower flange 44 adapted to besecured to load-applying frame 12.

A displacement sensor 46 is provided to measure displacement of anindenter carried by indenter apparatus 14 relative to a surface 32 ofsample 28 that is probed by the indenter. Preferably, a displacementsensor 46 is associated with fixture 24 or indenter mount 16 and, asillustrated, the sensor is an optical sensor mounted on stage surface26, and a corresponding mirror 48 is mounted on indenter mount 16.Optical displacement sensors, for example a combination photonic probeand photonic sensor sold by Photonics, Inc, are known. Equivalentdisplacement sensors of similar resolution are acceptable according tothis embodiment. Mirror 48 is positioned so as to reflect light emittedby sensor 46 back to the sensor. In this manner the sensor can determinethe displacement of the indenter relative to surface 32 of sample 28.The sensor operates via a standard technique by which the variation ofintensity between the emitted and received light is used to measure therelative motion between the probe and mirror 48 (thus displacement ofthe indenter relative to surface 32 of sample 28).

The vertical position of mirror 48 relative to indenter mount 16 can beadjusted, for example via a threaded coupling and lock nut, or viaslidable engagement and screw (not shown). In this manner the positionof mirror 48 relative to optical sensor 46 is adjustable to achieveoptimal distance therebetween for measurement of penetration into thesample. Additionally, the distance between the indenter assembly 14 andsurface 32 of sample 28 can be decreased at a controlled rate byadjusting the loading frame within which the system is positioned(described more fully below).

When a load is applied to surface 32 of sample 28 via the indenter, theapplied load is measured with load cell 18, and in conjunction withoptical sensor 46, a load/displacement curve can be obtained, both uponloading and unloading of the sample. The optical sensor 46 measures thedepth of penetration of the indenter of indenter assembly 14 intosurface 32 of sample 28 with an accuracy of at least about 0.5 μm, morepreferably at least about 0.2 μm, and most preferably at least about 0.1μm. The load cell 18 has a resolution of approximately at least about0.1 N. more preferably at least about 0.05 N, and more preferably atleast about 0.02 N. Load cell 18 can apply any of a wide variety ofloads, and the apparatus is preferably suited for conducting indentationtests in the region of from about 0.5 N to about 500 N.

The diameter of the indentation made is preferably less than about 1/5of the smallest diameter of the specimen (lateral dimension or height),in homogeneous materials. For layered materials, indentation depthshould be less than about one-tenth of the thickness of the layersampled to obtain properties of the layer, or greater than the thicknessto obtain properties of the substrate.

One aspect of the invention involves particularly accurate measurementvia a combination of stiffness and arrangement of the overall indenterapparatus. According to one embodiment, a distance X as illustrated inFIG. 2 between optical sensor 46 and the indenter is minimized (underthe constraint of specimen dimension). Minimizing the distance X betweenoptical sensor 46 and the indenter minimizes the effect of any deviationfrom normality or misalignment of load train, between the movement ofthe indenter relative to sample 28, on the accuracy of measurement.This, in combination with the stiffness of the apparatus, contributes toheightened accuracy. It has been found that, preferably, the distance Xis less than about 2 centimeters, more preferably less than about 1.5centimeters, and more preferably still less than about 1 centimeter. Ofcourse, dimension X must be great enough to accommodate a sample ofrelatively large lateral dimension, and may be larger than thesepreferred ranges. With stiff apparatus, greater dimensions can beaccommodated, and this is taken into account below.

According to one embodiment, the arrangement of apparatus 10 is suchthat the normality of movement of the indenter relative to surface 26 offixture 24 is within a prescribed range. As discussed, any deviationfrom normality is minimized by close proximity of optical sensor 46 andthe indenter. Deviation from normality of movement of the indenterrelative to surface 26 can be quantified in relation to this distance X.Preferably, if the deviation of normality of movement of the indenterrelative to surface 26 is assigned an angle value F, sin F will begreater than or equal to 0.05 μms divided by distance X between opticalsensor 46 and the indenter. More preferably, sin F will be greater thanor equal to 0.03 μms/X, and most preferably greater than about 0.015μms/X.

As discussed above, the invention provides very stiff apparatus, whichis particularly advantageous. Additionally, the apparatus is designed asa unit that is retrofittable into essentially any load-applyinglaboratory apparatus. As illustrated in FIG. 2, flange 22 of upper mount20 and flange 44 of base support 34 each are bolted to frame 12(described below) with bolts 50 that each pass through their respectiveflange and are threaded into frame 12. This is described more fullybelow with reference to FIG. 7.

It has been found that where threaded connections are made between eachportion of apparatus 10 that defines a separate component, that is, eachcomponent that is removable from an adjacent component using routinetools without cutting (for example upper mount 20 and frame 12, basesupport 34 and frame 12, threaded adjusting mount 36 and base support34, threaded adjusting mount 36 and fixture 24, bracket 30 and fixture24, indenter mount 16 and load cell 18, etc.), stiffness of theapparatus within preferred ranges can be achieved. In particular,apparatus having a stiffness great enough for accurate measurement ofmaterials as hard as ceramics, using a blunt indenter, in particular onehaving no portion that contacts the material having a radius ofcurvature of less than about 2 μm, is possible.

Preferably, all components of apparatus 10 (with the exception of, e.g.,mirror 48, displacement sensor 46, and the indenter) are made ofstainless steel.

Referring to FIG. 3, an indenter apparatus 14 for mounting a variety ofindenters is illustrated schematically in partial cross-section.Apparatus 14 includes a portion 52 adapted to be secured to indentermount 16. Portion 52 can include threads, and can be threaded into mount16, fit slidably into mount 16 and be secured therein with a lock bolt(not shown), or the like. Preferably, connection between indenterapparatus 14 and mount 16 is made via threaded coupling which is meantto include threading engagement between portion 52 and mount 16, orsliding engagement secured by a threaded locking mechanism. Apparatus 14includes a core 54 that is integral with portion 52, or securelyfastened thereto preferably threadingly. A threaded clamp 56 isconstructed and arranged to hold a spherical indenter 58 at its distalend. Clamp 56 threadingly engages core 54, to which pressure is appliedthrough load cell 18 via indenter mount 16. Core 54 includes a bottomsurface 60 that engages a top surface of the indenter. Thus, when clamp56 is fastened securely to the threaded core 54 such that the indenteris positioned firmly adjacent bottom surface 60 of core 54, any slackbetween the indenter and the load cell is minimized.

According to one preferred aspect of the invention, especially where aparticularly hard sample is to be analyzed, a lower portion 62 of core54 including surface 60 that impinges upon the indenter is particularlyhard. Preferably, portion 62 is at least 1.5 times as hard as the sampleto be analyzed, more preferably 1.75 times as hard, more preferably atleast twice as hard, and most preferably at least about 3 times as hard.Selection according to these criteria avoids indentation of core 54 withindenter 58 ("double indentation") which can lead to inaccuracy inpenetration measurement. Portion 62 can be made of, for example,tungsten carbide where remaining portions of the assembly 14 are made ofsteel (in addition to, or with the exception of, indenter 58 which cancomprise any indenter material). The thickness of portion 62, that is,the depth into core 54 in a direction away from indenter 58 that isdefined by the particularly hard material 62, is at least about 0.5 mm,more preferably, at least about 1.0 mm. Adequate stiffness typically canbe achieved within these ranges since the force applied by the indenteragainst the lower surface of portion 62 of core 54 during indentation israpidly diffused laterally with increasing depth into core 54.

It has been determined, in accordance with the invention, that accuracycan be maximized by cleaning indenter 58 and surface 60 of core 54 with,for example, alcohol or acetone prior to assembly of indenter apparatus14 and testing. Dirt particles between indenter 58 and surface 60 canact as indenters of indenter 58 and surface 60. Additionally, it can beadvantageous similarly to clean stage surface 26 and the surface ofsample 28 that is placed adjacent the stage surface.

FIG. 4 illustrates more particularly, in perspective view, a mechanismfor immobilizing a sample 28 on the upper surface 26 of fixture 24, thatis, mounting a sample 28 on the upper (stage) surface 26 of fixture 24securely in accordance with the invention. As illustrated, according toa preferred embodiment brackets 30 are placed across top surface 32 ofsample 28, and each includes a portion that is securely fastenable tofixture 24 via, for example, bolts 64 as illustrated. Where sample 28 issecured tightly to fixture 24 in accordance with the invention, anyslack between sample 28 and the top (stage) surface 26 of fixture 24 isminimized or eliminated. Preferably, the surface of the sample thatcontacts the stage surface is "lapped" prior to mounting to minimizemicromotion. It is another feature of this aspect of the invention that15 brackets 30 will prevent movement of the sample 28 away from stagesurface 26 during unloading, where the sample tends to adhere to theindenter. It is another feature that any movement laterally of sample 28relative to stage surface 26 is minimized or eliminated. One or more ofthese features, especially minimization of slack during loading andsecure downward fastening during unloading, eliminates or minimizes anyerroneous reflection of such movement in the load/displacement curveobtained via indenter probing of the sample. In many cases the bracketswill affect displacement on unloading to a much greater extent than onloading. Those of ordinary skill will recognize a variety of mechanismsfor securing sample 28 to fixture 24 in a manner that appliessignificant downward force on sample 28 in the direction of fixture 24,and these and other mechanisms are intended to be embraced by theinvention. The invention resides in the recognition of error inmeasurement that can result from lack of such secure fastening, and theprovision of a securing mechanism.

Brackets 30 can be positioned as close as feasible to the portion ofsurface 32 of sample 28 that is to be contacted by the indenter.Preferably, at least one bracket is spaced, and more preferably two arespaced, no more than 2 cm from the point of contact between the indenterand surface 32, more preferably no more than 1.5 cm, and more preferablystill no more than 1 cm therefrom.

One aspect of the invention allows for urging sample 28 against stagesurface 26 during application of load, via an indenter, to surface 32 ofsample 28. For example, load can be applied to the sample via theindenter and brackets 30 tightened against sample 28 at any point duringthe application of load. According to one embodiment, brackets 30 aretightened against sample 28 at maximum indenter applied load. This canresult in particularly precise measurement during unloading.

Another technique for immobilizing sample 28 on stage surface 26 is byadhering the sample to the stage surface. This can be done by coatingstage surface 26, or the bottom surface of sample 28, with an adhesiveprior to placing the sample on the stage surface, optionally urging thesample against the stage surface via, for example, clamping, andallowing the adhesive to adhere the sample to the stage surface.According to a more preferred arrangement, sample 28 is positioned atopstage surface 26 without adhesive between the sample and the stagesurface, followed by application of an adhesive to the interface of thesample and the stage surface about the perimeter of the sample. Theadhesive then is allowed to adhere the sample to the stage surface.

According to one embodiment of the invention, the rate at which load isapplied and released from the sample by the indenter is controlled so asto fall within certain preferred ranges, as it has been found inaccordance with the invention that control of this parameter can affectthe accuracy of measurement. In one embodiment, the invention involvesloading a sample with an indenter at a rate of less than about 2 μms persecond, more preferably less than about 1 μm per second, more preferablyless than about 0.5 μm per second, and most preferably less than about0.1 μm per second. In another embodiment, the rate of unloading is lessthan about 1 μm per minute, more preferably less than about 0.5 μm perminute, more preferably less than about 0.2 μm per minute, and morepreferably still less than about 0.1 μm per minute. A holding period ofat least thirty seconds is recommended at the level of maximum appliedload to ascertain time effect. Additionally, the rate of expansion orcontraction of the contact area is smaller than the velocity of elasticwaves in the material.

Another aspect of the invention involves particularly smooth applicationand/or release of load to a sample. The frame used to apply the load,according to this embodiment, applies and releases the load verysmoothly (e.g., a stepped motor is not used; servohydraulic testingmachines operated under displacement control typically cannot offersmooth enough motion for very accurate load/displacement analysis atunloading. It has been found that applying load with apparatus thatapplies and or releases load as smoothly as a screw-driven system, forexample, an electromechanical screw system, is most advantageous. Smoothrelease of load contributes to accuracy of measurement of Young'smodulus. Smooth application and/or release of load can be described interms of load applied and/or released smoothly as a function of time. Inparticular, a mechanism that has a load versus time relationship that isessentially linear, rather than a stepped load versus time curve, isdesired. Preferably, any "stepping" during loading and/or unloading willbe less than about 0.1 Newton per second, more preferably less thanabout 0.05 Newton per second, and more preferably still less than about0.01 Newton per second, depending on the material tested and maximumload softer materials require smoother release of load). An exemplary,non-limiting list of load-applying frames suitable for use with theinvention include those made by INSTRON (4505, 5567, 5566, 8562),Canton, Mass.; MTS, Eden Praine, Minn.; and MTS 2/GL Electromechanic. Awide range of loads can be applied using the system of the invention. Asdiscussed above, in preferred embodiments, the load applied is within arange between about 0.5N and 500 N, and a preferred frame can applyloads within this range.

One challenge in the use of sharp indenters is that in the measurementof polycrystalline materials, such as ceramics, where the size of eachgrain may be greater than the size of the tip of the indenter, it ispossible that the mechanical properties of only one grain will bemeasured at one time at sufficiently low loads. In such a case, it canbe advantageous to use a blunt indenter when bulk properties aremeasured. As used herein, the term "blunt" is given its usual meaning toinclude spherical indenters and the like and is given an additional,somewhat more precise definition as follows. Preferably, no portion ofthe blunt indenter surface that contacts the sample surface has a radiusof curvature of less than about 15 μm, more preferably less than about100 μm.

One feature of the invention is that a sample can be probed through arange of loads within microscale measurement through macro scalemeasurement whereby properties can be obtained. That is, with a singlemechanical testing arrangement, a combination of properties previouslyassumed to be obtainable only with separate nanoscale and macro scaleapparatus are determined. For very low loads, the classic theories ofelastic and elasto-plastic deformation no longer suffice to interpretresults accurately. Using the apparatus and methodology of theinvention, uncertainties encountered in many existing micro-indentationtechniques are circumvented since loads are low and at the same timehigh enough to probe average material properties.

In a preferred embodiment, indentation testing apparatus is adapted formounting in any existing load-applying frame that meets the requirementfor smooth application of load as described above. Referring to FIG. 2,indentation testing apparatus 10 is illustrated as mounted in aload-applying frame 12 such as an electromechanical testing system. Thisconfiguration is also shown in FIG. 7. Characteristics that make theapparatus adaptable for mounting in a variety of frames include mountingapparatus such as mounting flanges 44 and 22 as illustrated in FIG. 2.Apparatus 10 can be mounted on an existing frame, or removed from aframe and mounted on another frame, with routine mechanical operationusing known fasteners such as bolts 50 (FIG. 2). It is not critical thatdisconnection from a frame and re-attachment to another frame be carriedout by disconnecting and re-connecting flanges 22 and 44. Connection toan existing frame can be made via attachment of another portion ofapparatus 10 that is designed to be connectable to the frame. Asdiscussed above, threaded connection to the frame is preferred. Thisarrangement is distinguished from known, self-contained indentationtesting apparatus that is defined by an integral arrangement includingindenter and loading device as part of essentially a single unit that isnot designed to be separated and, indeed, could not be separated withoutsignificant effort using more than conventional tools, and seriouslycompromising accuracy of measurement when re-assembled. Indentationapparatus from known, self-contained units including an integral loadingdevice cannot be removed from such units without other-than-routineprocedures such as cutting or extensive disassembly, and typically arenot equipped with components that would render them readily mountable onan existing frame. Testing apparatus 10 can be installed in an existingframe rapidly (on the order of several hours to a day by one person ofordinary skill in the art).

When apparatus 10 is installed on a new frame and secured thereto,minimal recalibration of the displacement sensor, routine examination ofthe accuracy of the load cell, etc. is all that is needed. As discussedabove, when apparatus 10 is rigidly secured to the frame, preferably viathreaded fasteners, adjustable and other movable portions of theapparatus can be very securely immobilized, preferably also via threadedfasteners, so that the overall arrangement is very stiff.

Since known, self-contained indentation testing units typically includeload-applying equipment constructed in conjunction with the indentationtester as an integral unit, the apparatus of the present inventiontypically can be made much more inexpensively than prior art indentationtesting apparatus. In addition, loading apparatus of prior artarrangements is essentially useless for purposes other than applyingload in indentation testing. Thus, apparatus of the present inventiondoes not necessarily dominate a load-applying frame and prevent its usein other common mechanical tests such as tensile, compressive, andbending. The apparatus of the invention can be readily removed from aframe, the frame can be put to another use, and the apparatus returnedto the frame. This makes it a routine instrument of less delicatecharacter than, for example, the Nanoindenter™, capable ofreproducibility and standardization, and very economical with respect toamount of material, cost, and time spent to obtain mechanicalparameters.

By following the teachings described herein, a particularly preferredembodiment of indentation testing apparatus can be readily constructedthat is readily mountable in and removable from a load-applying frameusing common fasteners, that is capable of determining, from aload/depth relationship, one of Young's modulus, yield strength, tensilestrength, strain hardening exponent, and hardness, with less than about20% error. In a more preferred embodiment, such measurements can beroutinely made with less than about 10% error, and in a most preferredembodiment with less than about 5% error. Error is determined bycomparison to conventional macro scale tests.

Methodology

The invention also provides new methodology for indentation analysisthat involves direct derivatization of contact area fromload/displacement analysis.

The following description of this aspect of the invention is dividedinto methodology associated with sharp indenters and methodologyassociated with blunt indenters.

Sharp Indenters

The following methodology is based on dimensional analysis coupled withextensive finite element computations that take into account thethree-dimensional aspects of pyramidal indentations. Some of theequations below are known. For sharp indenters, the ratio of residualdepth (h_(r)) to maximum depth (h_(max)) defines the strain hardeningexponent (n). From the strain hardening exponent, the contact area atloading can be deduced from methodology described below. From theinitial slope (dP/dh) of the unloading portion of the load/depth dataand the contact area at unloading, the elastic modulus can be deduced asshown below. A correction for diamond tip compliance can be taken intoaccount. The yield strength can be deduced from the loading part of theload/depth data.

According to FIG. 5 (representative of a typical load/displacement curveusing a pyramidal indenter) the following values are determinedexperimentally during a single load/unload measurement: h_(r) /h_(max),dP/dh at P_(max), and P/h². Using h_(r) /h_(max), the parameter H/E isobtained according to equation 1. ##EQU2##

With the parameter H/E from equation 1, the maximum normalized contactarea A_(max) /h_(max) ² is given according to equation 2. ##EQU3##

Using dP/dh at h_(max) the combined elastic modulus E* can be obtainedaccording to equation 3. ##EQU4## where C* is 1.142 for the Vickersindenter geometry and 1.167 for Berkovich, and (ν) is the Poisson ratio(ν is approximately 0.3 for most materials, and can be obtained withaccuracy from the literature; specifically, ν=0.33 for metals, 0.25 forceramics, 1/(2√2) for optimum error; default value). To correct for thediamond tip compliance, equation 4 is used. ##EQU5## where the elasticmodulus of the diamond is taken as 900 GPa and its Poisson ratio as 0.2(E and E* in GPa).

It can be appreciated that accurate determination of contact area atloading is of paramount importance according to this methodology.

To compute yield strength the following ratio is examined: P_(max)/(A_(max) E tan β) where β=22° for Vickers and 24.7° for Berkovich. Ifthis ratio is less than 0.1, then yield strength is given by equation 5.##EQU6##

If the ratio above for computing yield strength is greater than or equalto 0.1, then the constant C=P/h² (Kick's law) is taken as follows: Forelasto-plastic behavior, equations 6 and 7 are used, together with thevalue of the parameter H/E, defined in equation 1, above. ##EQU7##

Mayer's hardness (P_(av)) is defined according to equation 8. ##EQU8##

To obtain the strain hardening exponent (n), equation 9 is used.##EQU9##

That is, according to equations 1-9 above, by measuring load versusdisplacement of essentially any type of material at load as low as about0.5 N or up to about 500 N, the area of contact between the indenter andthe sample surface, at loading, is calculated directly. Then, elasticmodulus is calculated, then yield strength and ultimate tensilestrength, and finally strain hardening exponent is derived.

Spherical Indenter

The following methodology results in derivation of contact area directlyfrom load/depth measurement, and subsequent calculation of mechanicalproperties. The process is based on the examination of the loadingportion of the load/depth measurement, the initial portion of which isassociated with the elastic modulus and the later portion of which isassociated with the fully plastic region. In certain cases the unloadingportion of the load/depth measurement may be useful as well.

The elastic modulus is computed by fitting the initial portion of theload/depth curve of FIG. 6 according to equation 10. ##EQU10## where Dis the diameter of the spherical indenter. From P and h values withinthe region of validity of the elastic solution on the curve (the regionof the curve according to P is proportional to h^(3/2)), E* can bedetermined.

To correct for the compliance of the indenter, equation 11 is used whereE' is the indenter's elastic modulus and ν' is the Poisson ratio.##EQU11##

To obtain the strain hardening exponent (n) the mainly plastic portionof the load/depth relation is obtained via equation 12, which is anexpression derived from Mayer's law in terms of load/depth relationship.##EQU12##

n is determined by measuring the slope of log P--log h, which gives thevalue of 1+n/2.

Contact area at maximum load (A_(max)) is derived from equation 13:

    A.sub.max =πDh.sub.max c.sup.2 =πa.sub.max.sup.2     Eq. 13

here a_(max) is the contact radius at maximum load and where c isrelated to strain hardening (n) by equation 14. ##EQU13##

Where the strain hardening exponent (n) is greater that 1/3.4,sinking-in at the perimeter of the indentation contact occurs. At n lessthan 1/3.4, pile-up occurs. Failure to take into account sinking-in andpile-up compromises accuracy in measurement of the true area of contactof the indenter under load.

Validity of the above methodology can be confirmed by ensuring thatmeasurements are taking place where the region of contact between theindenter and the sample is no more than 20% of the diameter of theindenter.

Next, the average pressure (P_(av) force divided by true contact area)is calculated according to equation 8 taking A_(max) from equation 13.

To compute the yield strength, first the characteristic strain atmaximum load is computed in accordance with equation 15. ##EQU14##

Yield strength is given by equation 16. ##EQU15##

The end of the elastic regime occurs at a point (h_(y), P_(y)) of theload/depth curve (FIG. 6) given by ##EQU16##

It may be so that the level at the yield initiation is too low and makesit difficult for the elastic modulus to be captured directly at loading(Eq. 10). Alternatively, the residual depth h_(r), (See FIG. 6) may beused as follows ##EQU17## Automated Set-Up for Experimentation andAnalysis

Illustrated in FIG. 7 is equipment that allows automated testing of asample and automated analysis of data obtained from testing. A controlpanel 66 can be used to manually control the loading frame 12, and loadapplied. A fast D/A converter 68 is connected via lead 70 todisplacement sensor 46 and via lead 72 to load cell 18 so as to acquireload and indentation depth measurements via a computer 74. LABVIEWsoftware can be used for data acquisition. Testing parameters, such asmaximum load and indenter type, are fed into the computer 74 which thendirectly acquires the data via the D/A converter and controls the testby standard general purpose interface bus (GPIB) connections 76. Thecomputer 74 also can be arranged to control an X-Y stage (not shown)upon which the specimen can be mounted, and other adjustable componentssuch as mirror 48 so that an entire set-up and testing procedure isessentially automated, and indentations can be performed at pre-selectedlocations serially.

An example computer system 74 is in FIG. 8. The computer 74 generallyincludes a processor 90 connected to a memory 94 via an interconnectionmechanism 92. An input device 98 is also connected to the processor andmemory system via the interconnection mechanism, as is an output device96.

It should be understood that one or more output devices 96 may beconnected to the computer 74. Example output devices include cathode raytube (CRT) displays, liquid crystal displays (LCD), printers, additionalstorage devices and control outputs via the GPIB connections 76, andcommunication devices such as a modem. It should also be understood thatone or more input devices 98 may be connected to the computer 74.Example input devices include GPIB connections 76, a keyboard, keypad,track ball, mouse, pen and tablet and communication device. It should beunderstood the invention is not limited to the particular input oroutput devices used in combination with the computer 74 or to thosedescribed herein.

The computer 74 may be a general purpose computer system which isprogrammable using a high-level computer programming language, such as"C," "Pascal" or "Visual Basic." The computer may also be speciallyprogrammed, using special purpose hardware. Additionally, the computer74 may be a multiprocessor computer system or may include multiplecomputers connected over a computer network.

In a general purpose computer system, the processor 90 is typically acommercially available processor, of which the series x86 processors,available from Intel, and the 680X0 series microprocessors availablefrom Motorola are examples. Many other processors are available. Such amicroprocessor executes a program called an operating system, of whichUNIX, DOS and VMS are examples, which controls the execution of othercomputer programs and provides scheduling, debugging, input/outputcontrol such as for the GPIB connections, accounting, compilation,storage assignment, data and memory management, communication controland related services. The processor and operating system define acomputer platform for which application programs in various programminglanguages may be written. It should be understood the invention is notlimited to a particular computer platform, particular processor, orparticular high-level programming language.

An example memory system 94 will now be described in more detail inconnection with FIG. 9. A memory system typically includes a computerreadable and writeable nonvolatile recording medium 100, of which amagnetic disk and tape are examples. The disk may be removable, known asa floppy disk, or permanent, known as a hard drive. Where the medium100, a disk, which is shown in FIG. 9, has a number of tracks, asindicated at 104, in which signals are stored, typically in binary form,i.e., a form interpreted as a sequence of one and zeros such as shown at106. Such signals may define an application program to be executed bythe microprocessor, or information stored on the disk to be processed bythe application program. Typically, in operation, the processor 90causes data to be read from the nonvolatile recording medium 100 into anintegrated circuit memory element 102, which is typically a volatile,random access memory such as a dynamic random access memory (DRAM) orstatic memory (SRAM). The integrated circuit memory element 102 allowsfor faster access to the information by the processor than does themedium 100. The processor generally manipulates the data within theintegrated circuit memory 102 and then copies the data to the medium 100when processing is completed. A variety of mechanisms are known formanaging data movement between the medium 100 and the integrated circuitmemory element 102, and the invention is not limited thereto. It shouldalso be understood that the invention is not limited to a particularmemory system 94.

A system for automated testing is shown in FIG. 10. This system includesthree interconnected modules, each of which may be implemented using acomputer program to run on a computer 74, each of which is an aspect ofthe invention. First module is a test design module 112 which receives,as an input, parameters of a test and the equipment to be used in thetest as indicated 110. Test design module then outputs control data 114which is then used in conducting a test. The control data 114 isreceived by a test conducting module 116 which outputs control signalsto the test equipment 117 to control its movement and to control thesensors and which in turn outputs the load/displacement data asindicated at 118. The load/displacement data 118 is applied to ananalysis module 120 which outputs an accurate measurement of the area ofcontact of the probe with the material, as indicated at 122. Thismeasurement may be used to determine the mechanical properties of thematerial being tested.

Each of the modules 112, 116 and 120 will now be described in moredetail in connection with FIGS. 11 through 15. The process of designinga test will be described first. In connection with FIGS. 11-13. FIGS.11-13 describe a preferred, optimized arrangement for selecting optimaltest parameters such as sphere diameter, maximum load, material of theindenter, and the like. The particular order and arrangement of thesteps involved could be altered by one of ordinary skill in the art toarrive at an equivalent result. The inventive nature of the processillustrated in FIGS. 11-13 involves using the criteria and equations setforth to arrive at the result, by whatever means.

The first step of defining a test is obtaining a specimen (step 130).Parameters of the test are then defined by an individual in step 132.Parameters to be defined include the maximum indentation load (P_(max)),the resolution of the system (P_(min), h_(min)). If a sharp indenterwill be used, a microstructural parameter (h_(l)) is defined. Thisparameter can be defined to be zero to indicate bulk evaluation.Microstructural evaluation can be indicated by a non-zero value for thisparameter. This value may indicate grain size or layer thickness, forexample. The type of indenter is also input. For example, the indentermay be sharp, such as a pyramidal indenter, or may be blunt. The size ofthe diamond tip (h_(s)) of a sharp indenter is input by the individual.For a blunt indenter, the yield strength or failure strength (σ_(y) ')and elastic properties (E', the Young's modulus of the blunt indenterand the Poisson ratio (ν') of the blunt indenter) are also input.Elastic and plastic properties of the specimen are then assumed,including the Young's modulus (E'), Poisson ratio (ν'), the yieldstrength (σ_(y) ') and fracture toughness K_(c).

Having defined the parameters of the indenter and the system, if bulkevaluation is to be performed (as determined by step 134), the combinedelastic modulus of the indenter and sample is determined according tothe assumed properties in step 136. If bulk evaluation is not to beperformed, but rather microstructural evaluation is to be performed, thegrain size or layer thickness is compared to the resolution of thesystem which needs to be larger than a tenth of the microstructuralfeature under consideration (i.e., as shown in steps 138 and 140) ofFIG. 11. If the system does not have enough displacement resolution(step 141) to perform the microstructural evaluation, the test must beredesigned in step 132. If there is enough displacement resolution inthe system, processing continues with step 136 described above.

Having computed the assumed combined effective elastic modulus of theindenter and sample based on the assumed properties of the specimen andthe input properties of the indenter, the control data for the test isthen determined, according to the indenter type as indicated in step142. The process for sharp indenters will be described below inconnection with FIG. 12. Some initial steps for blunt, for examplespherical indenters will continue to be described in connection withFIG. 11.

For a blunt indenter, the minimum diameter of the indenter to be used inthe test is then determined as a function of the maximum indentationlevel (P_(max)), the yield or failure strength in uniaxial compressionof the indenter, and the Poisson ratio of the indenter (step 144). Themeasured maximum indentation depth, (penetration or displacement) thenis determined as a function of this determined diameter in step 146.Additional parameters are determined in step 148. The diameter of theindenter below which "ring" cracking can develop in the sample (Dc') andthe diameter above which "radial" cracking could develop (Dc) aredefined in step 148 in relation with the input of the test. If thedetermined diameter is not between these two additional parameters, asdetermined in step 150, the mechanical properties of the indenter needto be changed as indicated at 152, which causes a request for aredefinition of the test in step 132. If the determined diameter D isacceptable, processing continues as described in more detail below inconnection with FIG. 13.

Referring now to FIG. 12, the determination of test parameters forconducting tests with sharp indenters will now be described. A valueP_(m) which evaluates the resistance against cracking in the sample isfirst calculated in step 160. If the test to be performed involvesmicroevaluation of the sample, as determined in step 162, it is thendetermined whether there is enough resolution in the system for the loadmeasurements. If the value P_(m) is not greater than the minimum loadthat can be applied to the sample, as determined in step 164, there isnot enough resolution for the load measurements (step 165) and the testshould be redefined in step 132. If there is enough load resolution, thetest is then performed in step 168 until the maximum measuredindentation depth and the maximum load applied to the sample with theindenter are less than the determined values h_(m) and P_(m).

For a bulk test with a sharp indenter (as determined in step 162), ifthe value P_(m) is greater than the load resolution of the system, thetest is then performed until the maximum load applied to the sample isless than the value P_(m), the maximum indentation depth is greater thanthe radius of the indenter tip, typically one tenth of a micron and isless than h_(s) as indicated at step 170. If P_(m) is not greater thanP_(min), as determined in step 172, there is not enough resolution forthe load measurements, as indicated at 174, and P_(min) should bedecreased (step 176). If the minimum load cannot be decreased, as may bedetermined in response to user input, the test is conducted using onlythe results on loading as indicated at 178. Otherwise, the test may beredefined by returning to step 132.

After conducting the test in either step 168, 170 or 178, processingcontinues with the analyzing of the results, which will be described inmore detail below in connection with FIGS. 13-15.

Determination of control parameters for a test with a spherical indenterwill now be described in connection with FIG. 13. This process continuesfrom step 150 in FIG. 11 with step 180 in FIG. 13 for determining thevalues D_(p) and h_(min) ' which define a load-displacement range wherethe test will capture the elastic response of the material. If h_(min) 'is not greater than h_(min) as determined in step 182, and if it ispossible to increase the load-depth resolution of the system, asdetermined in step 184 (possibly in response to user input) the test isredefined in step 132 of FIG. 11. Otherwise, the test is actuallyconducted in step 186, which will be described in more detail below. Ifh_(min) is less than h_(min) ', as determined in step 182, the valueD_(p) is compared to the calculated diameter. If D_(p) is not greaterthan the calculated diameter, as determined in step 188, and if themechanical properties of the indenter can be changed, as determined instep 190 (possibly in response to user input), the test is redefined byreturning to step 132, otherwise the test is conducted in accordancewith step 186 to be described in more detail below. If the value D_(c)is greater than the value D_(p) and if it is possible to use an indenterof diameter in the range of 70% to 100% of the value D_(p), asdetermined in step 194, the test is conducted in accordance with step196 to be described in more detail below. Otherwise the test isconducted in accordance with step 186, also to be described in moredetail below.

For D_(p) smaller than D_(c) and if 80% of the D_(p) value is less thanthe D_(c) value and if an indenter is available having a diameter in therange of 90% to 100% of the DC value (step 195), the test is conductedin accordance with step 196. Otherwise, the test is conducted inaccordance with step 186.

Given the parameters defined in the steps of FIGS. 11 through 13, thetest on the sample is conducted in any of steps 168, 170, 178, 186 and196. In step 186, a test is conducted until the minimum of P_(max) andh_(max) is obtained. Plasticity is analyzed upon loading and the Young'smodulus is calculated upon unloading. In step 196, the test is conducteduntil the minimum of P_(max) and h_(max) are obtained. All mechanicalproperties are calculated upon loading and unloading.

Each of these steps may be implemented using the test conducting module116 of FIG. 10. The test conducting module may be a general purpose testmodule which needs to be programmed to perform the test defined by thegiven and calculated parameters, or a custom program may be definedwhich receives the given and calculated parameters as input and whichperforms the step that a generic testing may perform. For example,generic control software may be programmed with a control program whichprompts a user for parameters of a test determined by the test designmodule 112. Suitable to systems for this control include FLAPS™ softwareof INSTRON, Series X or equivalent.

As described above in connection with FIG. 7, a displacement sensor 46and a load cell 18 are connected through the computer, for example, viaa digital to analog converter 68. The load and depth signals areinterpreted to obtain the elastic and plastic properties of the samplein step 198. These determined properties may be output to a displayand/or stored in the memory of the computer in step 200. If another testis needed or an alternative indenter shape is to be used, (step 202) thenew test can be designed by returning to step 132 (FIG. 11).

The interpretation of the load/depth signal for tests performed using asharp indenter will now be described in connection with FIG. 14. Thefirst step 210 involves computing the tangent elasto plastic modulus inaccordance with equation 1. Next, the maximum contact area is computedin step 212 according to equation 2. The combined Young's modulus isthen computed in step 214 according to equation 3. Corrections fordiamond tip compliance are then made in accordance with equation 4 instep 216. Hardness is then computed using equation 8 in step 218. Thecharacteristic strain is then computed (step 220) using the followingequation: ##EQU18## If the characteristic strain is less than 0.1, yieldand characteristic strength values are computed in step 222 according toequation 5. Otherwise, if the computed characteristic strain is greaterthan or equal to 0.1, yield and characteristic strength values arecomputed in step 224 according to equation 1 and equation 6 or 7. Aftercomputing the yield and the characteristic strength in steps 222 or 224,strain hardening is then computed according to equation 9 in step 226.

For a blunt indenter, such as a spherical indenter, the load/depthsignal is analyzed in accordance with FIG. 15. First, the combinedYoung's modulus is computed in step 230 according equation 10.Corrections for indenter compliance are then made in step 232 accordingto equation 11. The strain hardening exponent is then computed inaccordance with equation 12 in step 234. The log-log curve of theload/depth relationship is then analyzed to determine whether it islinear in step 236, hence whether the test is conducted in the fullyplastic regime and validates the theoretical plastic model assumed. Themaximum contact area, pile-up or sinking-in effects are then computed inaccordance with equations 13 and 14 in step 238. The average contactpressure is computed in step 240 according to equation 8. The maximumcharacteristic strain is then computed in accordance with equation 15 instep 242. Next, in step 244, the yield strength is computed according toequation 16. The region of elasticity is determined in step 246 usingequations 17 and 18. Finally, for the case where the ratio of P_(y) toP_(max) is smaller than 0.5, the unloading curve for the calculation forYoung's modulus is used in step 248, using equations 19 and 11.

The calculations performed in FIGS. 14 and 15 may be implemented as partof the analysis module 120 of FIG. 10. It should be understood that theload/displacement data will be stored in the memory system 94 of thecomputer 74 prior to analysis. Thus, since this data can be storedindefinitely, the analysis module may be used to analyze previouslyobtained results from other tests. Additionally, the test module, testexecution module and analysis modules may be located in differentcomputer systems and different locations.

The above methodology can be programmed into a computer such as shown inFIGS. 7-9 by one of ordinary skill in the art so that with a singlecommand or series of commands, one, several, or all of thedeterminations described above can be carried out. Known mechanicalproperties of materials can be installed on the computer in the form ofa data base so that the apparatus can help the user in the definitionsproposed in step 132 of FIG. 11.

EXAMPLES

The function and advantages of these and other embodiments of thepresent invention will be more fully understood from the examples below.The following examples are intended to illustrate the benefits of thepresent invention, but do not exemplify the full scope of the invention.

Example 1

Determination of Young's Modulus (E) in a Ceramic Material.

Yttria-tetragonal zirconia polycrystalline material was selected assample 28 and mounted on a stage surface 26 of fixture 24 as illustratedin the figures. Brackets 30 were applied and the sample was firmlyfastened to the stage via engagement of bolts 64 into fixture 24. Adiamond Vickers pyramidal indenter was selected. The ceramic sample hada top surface 32, facing the indenter, which had been finely polished. Aloading rate of about 5 μm per second was applied to the sample up toapproximately 1 N. The sample was unloaded at a rate of about 2 μm perminute. The resultant plot of load versus displacement appears in FIG.16. Calculation of Young's modulus (E) was obtained using equation 3.

In this case h_(max) equals 1.55 μm and dP/dh is 1.34 N/μm. From thesemeasurements, the value of E was estimated to be 187 GPa, which compareswell with the known value of 200 GPa for this material.

Example 2

Measurement and Calculation of Strain Hardening Exponent (n) of Nickel(Spherical Indenter).

A load/indentation test of a polished nickel sample with a WC bluntindenter of 1.587 mm diameter, Young's modulus 610 GPa, hardness of 17GPa, and Poisson ratio of 0.3 was carried out. To calculate hardnessexponent (n) the inventive formulation of Equation 12 was used. A plotof log P versus log h became a straight line (for h>3 μm) in the fullyplastic regime as shown in FIG. 17. Using this data, n was determined tobe 0.19. This result is in good agreement with the value of 0.21obtained for pure nickel using tensile tests.

Example 3

Evaluation of Yield Strength of Nickel With Spherical Indenter

Experimentation was carried out as in example 1 but using the sphericalindenter of example 2. Mean value of P_(av) was 0.73 GPa according toequation 8. Equation 15 gave yield strength of 153 MPa which is in verygood agreement with tensile tests where yield strength was measured tobe 148 MPa.

Example 4

Assessment of the Loading Portion of the Load/Depth Response of VickersIndentation on a Nickel Sample

Experimentation was carried out as in example 1. From Examples 2 and 3,the yield strength and elastic modulus were computed according to thetheory of the spherical indentation. Equation 6 then was used to providethe theoretical load/depth curve 78 of FIG. 18. Curves 80 and 82represent the boundaries of all experimental data, representing tenexperiments on Nickel using a Vickers indenter. The theoretical curvefalls well within the bounds of experimentation.

Those skilled in the art would readily appreciate that all parameterslisted herein are meant to be exemplary and the actual parameters willdepend upon the specific application for which the methods and apparatusof the present invention are being used. It is, therefore, to beunderstood that the foregoing embodiments are presented by way ofexample only and that, within the scope of the appended claims andequivalents thereto, the invention may be practiced otherwise than isspecifically described.

What is claimed is:
 1. A computer system for computing an area ofcontact between an indenter and a surface of a sample to which a load isapplied via the indenter, comprising:input means for receiving signalsindicative of a load applied to a sample surface via an indenter andindicative of a depth of penetration of the indenter into the sample;and means for computing maximum contact area between the indenter andthe sample surface using the signals received by the input means, wheresaid means for computing computes said contact area from signalsreceived from a single load/unload cycle.
 2. A computer system as inclaim 1, further comprising means for computing combined Young's modulusof the indenter and the sample, and means for computing Young's modulusof the sample.
 3. A computer system as in claim 1, further comprisingmeans for computing hardness of the sample.
 4. A computer system as inclaim 1, further comprising means for computing yield strength of thesample.
 5. A computer system as in claim 4, further comprising means forcomputing strain hardening exponent of the sample.
 6. A computer systemas in claim 1, wherein the input means is a computer memory.
 7. Acomputer system as in claim 1, wherein the input means is connected to acomputer memory.
 8. A computer system as in claim 1, wherein saidmaximum contacted area computed by the computing means includes anyeffects of pile-up and sinking-in of a sample material duringpenetration of the indenter into the sample.
 9. A computer system forcomputing an area of contact between an indenter and a surface of asample to which a load is applied via the indenter, comprising:anacquisition module having an input for receiving values of load appliedto a sample surface via an indenter and depth of penetration of theindenter into the sample and an output; and an analysis module having aninput for receiving said values of load and depth from the output of theacquisition module, and an output providing a signal indicative ofmaximum contact area between the indenter and the sample surface, wheresaid analysis module accounts for any effects of pile-up and sinking-inof a sample material during penetration of the indenter into the samplein providing the output signal indicative of maximum contact area.
 10. Acomputer system as recited in claim 9, the analysis module furthercomprising an output providing a signal indicative of Young's modulus ofthe sample.
 11. A computer system as recited in claim 9, the analysismodule further comprising an output providing a signal indicative ofhardness of the sample.
 12. A computer system as recited in claim 9, theanalysis module further comprising an output providing a signalindicative of yield strength of the sample.
 13. A computer system asrecited in claim 12, the analysis module further comprising an outputproviding a signal indicative of strain hardening exponent of thesample.
 14. A computer system as in claim 9, wherein said analysismodule can compute said contact area from values of load and depthreceived from the acquisition module for a single load/unload cycle. 15.A computer system for computing an area of contact between an indenterand a surface of a sample to which a load is applied via the indenter,comprising:input means for receiving signals indicative of a loadapplied to a sample surface via an indenter and indicative of a depth ofpenetration of the indenter into the sample; and means for computingmaximum contact area between the indenter and the sample surface, saidmeans for computing maximum contact area including means for accountingfor any effects of pile-up and sinking-in of a sample material duringpenetration of the indenter into the sample, using the signals receivedby the input means.
 16. A computer system as in claim 15, wherein saidmeans for computing maximum contact area computes said contact area fromsignals received from a single load/unload cycle.
 17. A computer systemfor computing an area of contact between an indenter and a surface of asample to which a load is applied via the indenter, comprising:anacquisition module having an input for receiving values of load appliedto a sample surface via an indenter and depth of penetration of theindenter into the sample and an output; and an analysis module having aninput for receiving said values of load and depth from the output of theacquisition module, and an output providing a signal indicative ofmaximum contact area between the indenter and the sample surface, wheresaid analysis module computes said contact area from values of load anddepth received from the acquisition module for a single load/unloadcycle.
 18. A computer system as in claim 17, wherein said maximumcontact area includes any effects of pile-up and sinking-in of a samplematerial during penetration of the indenter into the sample.